Hidden-Variable Models for Discriminative Reranking Jiawen, Liu Spoken Language Processing Lab, CSIE National Taiwan Normal University Reference: Hidden-Variable Models for Discriminative Reranking. Terry Koo, Michael Collins, EMNLP, Parse Reranking with WordNet Using a Hidden- ​ Variable Model. Terry Koo and Michael Collins, M. ​ Eng Thesis, Massachusetts Institute of Technology, Cambrige, MA, USA

National Taiwan Normal University Outline Introduction The hidden-variable model Local feature vectors Training the model Hidden-value domains and local features Experimental Results Applying the Model to Other NLP Tasks Empirical Analysis of the Hidden Values Conclusions and Future Research 2

National Taiwan Normal University Introduction-1 A number of recent approaches in statistical NLP have focused on reranking algorithms. The success of reranking approaches depends critically on the choice of representation used by the reranking model. Typically, each candidate structure is mapped to a feature-vector representation. This paper describes a new method for the representation of NLP structures within reranking approaches. Their method involves a hidden-variable model, where the hidden variables correspond to an assignment of words to either clusters or word-senses. Lexical items are automatically assigned their hidden values using unsupervised learning within a discriminative reranking approach. 3

National Taiwan Normal University Introduction-2 They make use of a conditional log-linear model for their task. Formally, hidden variables within the log–linear model consist of global assignments, where a global assignment entails an assignment of every word in the sentence to some hidden cluster or sense value. The number of such global assignments grows exponentially fast with the length of the sentence being processed. Training and decoding with the model requires summing over the exponential number of possible global assignments They show that the required summations can be computed efficiently and exactly using dynamic–programming methods under certain restrictions on features in the model. 4

National Taiwan Normal University Introduction-3 Their model has the ability to alleviate data sparsity issues by learning to assign words to word clusters, and can mitigate problems with word–sense polysemy by learning to assign lexical items to underlying word senses based upon contextual information. 5

National Taiwan Normal University The hidden-variable model-1 Each sentence s i for i = 1…n in their training data has a set of n i candidate parse trees t i,1,..., t i,n i, which are the output of an N –best baseline parser. They define t i,1 to be the parse with the highest F–measure for sentence s i. Given a candidate parse tree t i,j, the hidden– variable model assigns a domain of hidden values to each word in the tree. Formally, if t i,j spans m words then the hidden–value domains for each word are the sets H 1 (t i,j ),…, H m (t i,j ). A global hidden–value assignment, which attaches a hidden value to every word in t i,j, is written h= (h 1,…,h m ) H(t i,j ), where H(t i,j ) = H 1 (t i,j ) ×…×H m (t i,j ) is the set of all possible global assignments for t i,j. 6

National Taiwan Normal University The hidden-variable model-2 7

National Taiwan Normal University The hidden-variable model-3 They define a feature–based representation Φ(t i,j, h). Each component of the feature vector is the count of some substructure within (t i,j, h). For example, They use a parameter vector Θ R d to define a log–linear distribution over candidate trees together with global hidden–value assignments: 8

National Taiwan Normal University The hidden-variable model-4 By marginalizing out the global assignments, they obtain a distribution over the candidate parses alone: The loss function is the negative log-likelihood of the training data-with respect to Θ : 9

National Taiwan Normal University Local feature vectors-1 Note that the number of possible global assignments grows exponentially fast with respect to the number of words spanned by t i,j. This poses a problem when training the model, or when calculating the probability of a parse tree through Eq. 2. This section describes how to address this difficulty by restricting features to sufficiently local scope. The restriction to local feature–vectors makes use of the dependency structure underlying the parse tree t i,j. Formally, for tree t i,j, they define the corresponding dependency tree D(t i,j ) to be a set of edges between words in t i,j, where (u, v) D(t i,j ) if and only if there is a head–modifier dependency between words u and v. 10

National Taiwan Normal University Local feature vectors-2 If w, u and v are word indices, they introduce single–variable local feature vectors and pairwise local feature vectors. The global feature vector Φ(t i,j, h) is then decomposed into a sum over the local feature vectors: 11

National Taiwan Normal University Local feature vectors-3 In their implementation, each dimension of the local feature vectors is an indicator function signaling the presence of a feature, so that a sum over local feature vectors in a tree gives the occurrence count of features in that tree. For instance, 12

National Taiwan Normal University Training the model-1 The gradient of the loss function is given by: where Using the feature–vector decomposition in Eq. 4, they can rewrite the key functions of as follows: 13

National Taiwan Normal University Training the model-2 where and are marginalized probabilities and Z i,j is the associated normalization constant: The three quantities above can be computed with belief propagation (Yedidia et al., 2003), a dynamic–programming technique that is efficient and exact when the graph D(t i,j ) is a tree. 14

National Taiwan Normal University Hidden-value domains and local features-1 Each word in a parse tree is given a domain of possible hidden values by the hidden–variable model. In particular, they will see how different definitions of the domains give rise to the three main model types: –Clustering –Refinement –Mapping into a pre–built ontology such as WordNet. To splits each word into a domain of three word–sense hidden values. –Each word receives a domain of hidden values that is not shared with any other word. –The model is then able to distinguish several different usages for each word, emulating a refinement operation. 15

National Taiwan Normal University Hidden-value domains and local features-2 To split each word’s part–of–speech tag into several sub–tags. –This approach assigns the same domain to many words. –The behavior of the model then emulates a clustering operation. In their experiments, they made use of features such as those in Figure 2 in combination with the following four definitions of the hidden–value domains. –Lexical (Refinement) Each word is split into three sub–values. –Part–of–Speech (Clustering) The part–of–speech tag of each word is split into five sub–values. The word shares would be assigned the domain {NNS 1,..., NNS 5 }. –Highest Nonterminal (Clustering) The highest nonterminal to which each word propagates as a headword is split into five sub–values. The word bought yields domain {S 1,..., S 5 } 16

National Taiwan Normal University Hidden-value domains and local features-3 –Supersense (Pre–Built Ontology) They borrow the idea of using WordNet lexicographer filenames as broad “supersenses”. For each word, they split each of its supersenses into three sub– supersenses. If no supersenses are available, we fall back to splitting the part–of– speech into five sub–values. shares has the supersenses {noun.possession 1, noun.act 1, noun.artifact 1,... noun.possession 3, noun.act 3, noun.artifact 3 }. in does not have any WordNet supersenses, so it is assigned the domain {IN 1,..., IN 5 }. 17

National Taiwan Normal University Hidden-value domains and local features-4 18

National Taiwan Normal University The final feature sets They created eight feature sets by combining the four hidden–value domains above with two alternative definitions of dependency structures –Standard head–modifier dependencies –Sibling dependencies For instance –The head–modifier dependencies produced by the tree fragment in Figure 2 are (bought, shares), (bought, in), and (bought, yesterday) –The sibling dependencies are (bought, shares), (shares, in), and (in, yesterday). 19

National Taiwan Normal University Mixed Models The different hidden–variable models display varying strengths and weaknesses. They created mixtures of different models using a weighted average: where Z(s i ) is a normalization constant that can be ignored. 20

National Taiwan Normal University Experimental Results-1 They trained and tested the model on data from the Penn Treebank. For each of the eight feature sets, they used the stochastic gradient descent method to optimize the parameters of the model. They created various mixtures of the eight models, testing the accuracy of each mixture on the secondary development set. Their final model was a mixture of three of the eight possible models: –supersense hidden values with sibling trees –lexical hidden values with sibling trees –highest nonterminal hidden values with normal head–modifier trees. 21

National Taiwan Normal University Experimental Results-2 Their final tests evaluated four models –the Collins (1999) base parser, C99. –the Collins (2000) reranker, C2K. –a combination of the C99 base model with the three models, MIX. –augmenting MIX with features from the method in C2K, MIX+. 22

National Taiwan Normal University Applying the Model to Other NLP Tasks-1 To summarize the model, the major components of the approach are as follows: –They assume some set of candidate structures t i,j, which are to be reranked by the model. Each structure t i,j has n i,j words w 1,..., w n i,j, and each word w k has a set H k ( t i,j ) of possible hidden values. –They assume a graph D(t i,j ) for each t i,j that defines possible interactions between hidden variables in the model. –They assume some definition of local feature vectors, which consider either single hidden variables, or pairs of hidden variables that are connected by an edge in D(t i,j ). There is no requirement that the hidden variables only be associated with words in the structure –In speech recognition hidden variables could be associated with phonemes rather than words 23

National Taiwan Normal University Applying the Model to Other NLP Tasks-2 NLP tasks other than parsing involve structures t i,j that are not necessarily parse trees. –In speech recognition candidates are simply strings (utterances). –In tagging tasks candidates are labeled sequences. As a final note, there is some flexibility in the choice of D(t i,j ). –In the more general case where D(t i,j ) contains cycles 24

National Taiwan Normal University Empirical Analysis of the Hidden Values-1 Their model makes no assumptions about the interpretation of the hidden values assigned to words. During training, the model simply learns a distribution over global hidden– value assignments that is useful in improving the log–likelihood of the training data. However, they expect that the model will learn to make hidden–value assignments that are reasonable from a linguistic standpoint. They established a corpus of parse trees with hidden–value annotations, as follows. –They find the optimal parameters Θ* on the training set. –For every sentence s i in the training set, they then use to find, the most probable candidate parse under the model. –They use to decode, the most probable global assignment of hidden values, for each parse tree. 25

National Taiwan Normal University Empirical Analysis of the Hidden Values-2 They created a corpus of pairs for the feature set defined by part– of– speech hidden–value domains and standard dependency structures. 26

National Taiwan Normal University Conclusions and Future Research The hidden–variable model is a novel method for representing NLP structures in the reranking framework. They can obtain versatile behavior from the model simply by manipulating the definition of the hidden–value domains, and they have experimented with models that emulate word clustering, word refinement, and mappings from words into an existing ontology. Future work may consider the use of hidden–value domains with mixed contents. Another area for future research is to investigate the use of unlabeled data within the approach. Finally, future work may apply the models to NLP tasks other than parsing. 27